It's a nightmare. Of course. You'll rarely be so lucky as to have your basis factors also be eigenvectors.

这是一场噩梦 当然可以 你很少会这么幸运 因为你的基因子也是特征向量。

Take a look at what happens if our basis vectors just so happened to be eigenvectors, e.g.

看一下如果基向量恰好是特征向量会发生什么。

The only eigen value is two, but every vector in the plane gets to be an eigenvector with that eigen value.

唯一的特征值是2 但是平面上的每个向量都是具有这个特征值的特征向量。

Vectors, core topics in linear algebra, like determinants and eigenvectors, seem indifferent to your choice of coordinate systems.

向量 线性代数的核心主题 像行列式和特征向量 似乎与你选择的坐标系无关。

What we want is a non zero eigenvector.

我们要的是一个非零特征向量。

And the way to interpret this is that all the basis vectors are eigenvectors, with the diagonal entries of this matrix being their eigen values.

解释这个的方法是所有的基向量都是特征向量 这个矩阵的对角线元素是它们的特征值。

What this expression is saying is that the matrix vector product A times V gives the same result as just scaling the eigenvector V by some value lambda.

这个表达式说的是矩阵向量乘积A乘以V得到的结果和特征向量V乘以某个值是一样的。

Confusion about agon stuffs usually has more to do with the shaky foundation in one of these topics than it does with eigenvectors and eigen values themselves.

对正交的困惑通常更多的是与这些主题中的一个不稳定的基础有关 而不是与特征向量和特征值本身有关。

In fact, most of the concepts I've talked about in this series, with respect to vectors as arrows in space, things like the dot product or eigenvectors have direct analogs.

事实上 我在这个系列中讲过的大部分概念 关于空间中的箭头向量 像点积或者特征向量都有直接的类似物。